All atomic nuclei with an odd atomic mass or an odd atomic number possess a nuclear magnetic moment. Nuclear magnetic resonance (NMR) is a phenomenon exhibited by this select group of atomic nuclei (termed "NMR active" nuclei), and is based upon the interaction of the nucleus with an applied, external magnetic field. The magnetic properties of a nucleus are conveniently discussed in terms of two quantities: the gyromagnetic ratio (.gamma.); and the nuclear spin (I). When an NMR active nucleus is placed in a magnetic field, its nuclear magnetic energy levels are split into (2I+1) non-degenerate energy levels, which are separated from each other by an energy difference that is directly proportional to the strength of the applied magnetic field. This splitting is called the "Zeeman" splitting and is equal to .gamma.hH.sub.o /2.pi., where h is Plank's constant and H.sub.o is the strength of the magnetic field. The frequency corresponding to the energy of the Zeeman splitting (.omega..sub.o =.gamma.H.sub.o) is called the "Larmor frequency" and is proportional to the field strength of the magnetic field. Typical NMR active nuclei include .sup.1 H (protons), .sup.13 C, .sup.19 F, and .sup.31 P. For these four nuclei I=1/2, and each nucleus has two nuclear magnetic energy levels.
When a bulk sample containing NMR active nuclei is placed within a magnetic field, the nuclear spins distribute themselves amongst the nuclear magnetic energy levels in accordance with Boltzmann's statistics. This results in a population imbalance between the energy levels and a net nuclear magnetization. It is this net nuclear magnetization that is studied by NMR techniques.
At equilibrium, the net nuclear magnetization is aligned parallel to the external magnetic field and is static. A second magnetic field perpendicular to the first and rotating at, or near, the Larmor frequency can be applied to induce a coherent motion of the net nuclear magnetization. Since, at conventional field strengths, the Larmor frequency is in the megahertz frequency range, this second field is called a "radio frequency" or RF field.
The coherent motion of the nuclear magnetization about the RF field is called a "nutation." In order to conveniently deal with this nutation, a reference frame is used which rotates about the z-axis at the Larmor frequency. In this "rotating frame" the RF field, which is rotating in the stationary "laboratory" reference frame, is static. Consequently, the effect of the RF field is to rotate the now static nuclear magnetization direction at an angle with respect to the main static field direction. By convention, an RF field pulse of sufficient length to nutate the nuclear magnetization through an angle of 90.degree., or .pi./2 radians, is called a ".pi./2 pulse."
A .pi./2 pulse applied with a frequency near the nuclear resonance frequency will rotate the spin magnetization from an original direction along the main static magnetic field direction into a plane perpendicular to the main magnetic field direction. Because the RF field and the nuclear magnetization are rotating, the component of the net magnetization that is transverse to the main magnetic field precesses about the main magnetic field at the Larmor frequency. This precession can be detected with a receiver coil that is resonant at the precession frequency and located such that the precessing magnetization induces a voltage across the coil. Frequently, the "transmitter coil" employed for applying the RF field to the sample and the "receiver coil" employed for detecting the magnetization are one and the same coil.
In addition to precessing at the Larmor frequency, in the absence of the applied RF energy, the nuclear magnetization also undergoes two relaxation processes: (1) the precessions of various individual nuclear spins which generate the net nuclear magnetization become dephased with respect to each other so that the magnetization within the transverse plane loses phase coherence (so-called "spin-spin relaxation") with an associated relaxation time, T.sub.2, and (2) the individual nuclear spins return to their equilibrium population of the nuclear magnetic energy levels (so-called "spin-lattice relaxation") with an associated relaxation time, T.sub.1.
The nuclear magnetic moment experiences an external magnetic field that is reduced from the actual field due to a screening from the electron cloud. This screening results in a slight shift in the Larmor frequency (called the "chemical shift" since the size and symmetry of the shielding is dependent on the chemical composition of the sample).
Since the Larmor frequency is proportional to the field strength, it is generally desirable to insure that the main magnetic field and the RF magnetic field are spatially homogeneous, at least in the sample area, so that all parts of the sample generate an NMR signal with the same frequency. However, there are some known applications of NMR techniques for which it is desirable to establish a magnetic field gradient across the sample: examples of such applications include NMR imaging, molecular diffusion measurements, solvent suppression, coherence pathway selection and multiple-quantum filters.
A conventional method of applying such gradients is to use special gradient coils that create a B.sub.O field in addition to the coils which generate the main static field and the coils which generate the RF magnetic field. These special coils are often located in the NMR probe and generate a magnetic field gradient called a B.sub.O gradient which has at least one field component that has a direction parallel to the main static field direction, but has an amplitude which varies as a function of spatial position. All of the aforementioned NMR applications have been demonstrated utilizing a B.sub.O gradient. The coils which generate the B.sub.O gradients are well-known and not of significance with regards to the invention.
Another method of generating a magnetic field gradient is to use special RF field coils to generate a magnetic field gradient called a B.sub.1 gradient which has at least one component with a direction lying in the plane perpendicular to the main static field direction and a magnitude that varies across the plane. All of the previously-mentioned applications have also utilized such a B.sub.1 gradient.
There have been three different prior art approaches that used B.sub.1 gradient coils in high-resolution spectroscopy. The first of these approaches was to use the inherent inhomogeneity of a standard RF coil to generate a non-homogeneous field. Consequently, this approach did not use true gradients. The approach is described in detail in an article entitled "The Selection of Coherence-transfer Pathways by Inhomogeneous z Pulses", C. J. R. Counsell, M. H. Levitt and R. R. Ernst, Journal of Magnetic Resonance, v. 64, pp. 470-478.
A second approach utilized a special "straddle" coil to generate the required gradient. This approach is described in detail in an article entitled "Spatial Localization Using a `Straddle Coil`", Journal of Magnetic Resonance, v. 77, p. 101 (1988).
A third approach used a surface coil to generate the gradient. This approach is described in detail in an article entitled "Self-Diffusion Measurements Using a Radiofrequency Field Gradient", D. Canet, B. Diter, A. Belmajdoub, J. Brondeau, J. C. Boubel and K. Elbayed, Journal of Magnetic Resonance, v. 81, pp. 1-12 (1989).